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In sequence P, P4 and P5 are 11 and 9 respectively. Each [#permalink]
05 Sep 2004, 22:34

In sequence P, P4 and P5 are 11 and 9
respectively. Each term after the first two terms
in sequence P is either the sum of the previous
two terms if that sum is odd, or half the sum of
the previous two terms if the sum is even. What
is the largest possible product of P1 and P2?

Greatest product I found was actually 105. I just drew a tree with possible answers.
P1 = 8
P2 = 5
P3 = 13
P4 = 9
P5 = 11
In the above, P1*P2 would be 40 and A would be the answer.
However, another possible answer would be:
P1 = 21
P2 = 5
P3 = 13
P4 = 9
P5 = 11
Here, P1*P2 would be 105 and would actually be the real answer. _________________

P5 is odd, so P5 = P3+P4 -> since P5 is odd, so it will be the sum of the previous two terms 9 = P3+11 P3 = -2

If you examine the question carefully, it says that if the sum is odd, then the term is also odd. It doesn't say that if the term is odd, it must have come from an odd sum. In other words, if the sum is even, half of this can be an odd term.

can anyone explain how they got the numbers for the terms in the sequence ? It seems there a number of possibilites, depending of if you decide the sum to be odd or even.

I think first you can begin by
drawing the set-up, something
like this: _ _ _ 11 9.

You are told that, by the rules of the sequence, the fifth term, 9, is found either by summing 11 and the third term or by summing the two
terms and cutting them in half. Since it is impossible to add a positive integer to 11 to get 9, we must be adding an integer to 11 to get 18.

Therefore the third term must equal 7. Your scratch paper should
now look like this: _ _ 7 11 9. Now, the second term + 7 must equal either 22 or 11. If it equaled 22, the second term would have to be 15, but then there would be no legal possible value for the first term, so the two terms must sum to 11.

Therefore, the second term is 4. Your scratch paper now looks like _ 4 7 11 9. Then by the same logic used to this point, the first term equals either 10 (to sum to 14) or 3 (to sum to 7).

The largest possible product of the first two terms is therefore 40 or answer choice (A).

from now on, I will try to post 4-5 questions everyday and I'll give the answer at the end of the day...I want to make my contribution to this website....good job intr3pid

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